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How to Interpret Box and Whisker Plots

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How to Interpret Box and Whisker Plots

Box and Whisker Plots, so the problem tells us to first use the data to make a box and whisker plot and number two it asks us what is the link of the box and whisker plot tell you about the data. Alright, so first of all let’s look at making a box and whisker plot. So a box of whisker plot shows the distribution, okay, of data okay? So a box and whisker plot shows the distribution of data and it separates data into four equal parts okay? Alright, although the parts usually differ in link each part contains ¼ of the data okay? Now, the middle half is represented by a box so in the box of whisker plot, okay, it’s divided into four equal parts right? But the middle half, okay, is (oops) the middle half okay, is represented by a box, okay, with a vertical line at the median okay? Alright, now the lower fourth and the upper fourth, okay, are represented by the whisker, okay, our whiskers okay and that extends to the smallest and largest value. Alright so as we do this you’ll what we are talking about here with the box and whisker plot okay? So the first step we need to do to make a box and whisker plot with this data, okay, is we need to order the data and find the smallest value. The first quartile median, third quartile and the largest okay so I am going to go ahead and I have rewritten this data, okay, so it is in order, okay? So we ordered the data, okay, from smallest to largest and then we find this smallest value the first quartile median, third quartile and largest value so here we have our smallest value, 17, our largest value is 56, okay? Our median, okay, is the middle number so this is, a 38 is our median okay? Now, the first quartile we need to find so it is the middle—the median of the lower half so if this is our median, okay, we go to our lower half which is this side is our lower okay and we have two middle numbers okay in our lower half so we have to take the median of that or the average. Okay, so now we have to (I am sorry) we’ve take the mean of these two values to find the median of our lower quartile. So to find it we are going to take 22 plus 22 and divide it by a total number of values in it which is 2 and we got 22 okay? Now, we are going to take the median of our upper quartile, okay, which is this side alright? So the arms are the upper half alright to find the upper quartile right? So I mean to find our third quarter—excuse me—so—I am in a backup for a second. So 22, alright, is going to be is our first quartile so let me make that clear. So our first quartile is 22 okay? Now our median like we said was 38 right? We said our smallest value is 17, our first quartile is 22, our median is 38 now we are going find our third quartile, okay? So our third quartile we are going to look at our upper half here and we are going to find the median. Okay, well again we have an even number of values so we have two middle values so we are going to take the average of this two. Alright, so new are going to take 50 plus 51 and divide it by 2 so you have choose a values in that status side and we got 50.5, so our third quartile is 50.5 okay? And our largest value we said is 56 okay? So now we have to check for outliers ok? So the data that are more —remember when you are finding outliers, okay, the data —data that are more than 1.5 times, okay, the value of the interquartile range, okay so it is times the value of the interquartile range beyond the quartiles are called your outliers okay? So when you are finding your interquartile range, alright, it is your upper quartile minus your lower quarter okay? So our upper quartile, alright, our upper quartile is our third quartile so it is 50.5 okay so our upper quartile is 50.5 and our lower quartile is our first quartile which is 22, okay? Alright, so now we are going to find the difference and that would give us 28.5 and that is our interquartile range. So now we need to find our outliers right? So it is 1.5 times the interquartile range so I am going to take my interquartile range, 28.5 and I amgoing to multiply that 1.5 and that gives me 42.75, okay? So now we need to find the limits, okay, so now we need to find our limits of outlier okay? So to find the limits, we are going to subtract, okay, 42.75 from my lower quartile okay? So I am going to take 22 okay which is our lower quartile right and I am going to subtract 42.75 and I get negative 20.75 and then we need to find the upper limits right? So I am going to add this time 42 to 50.5, so I am going to take 50.5 and I am going to add 42.75 and I get 93.25, okay? So when you are finding your limits, you are going to take your—when you are finding your outliers you are going to take this product, okay, and then you are going to subtract, okay? You are going to subtract from your lower quartile and then you are going to take this same one and you are going to add to your upper quartile, okay, and that is going to how you are going to find in your limits okay? So, the limits for these outliers are negative 20.75 and 93.25 so there is no value okay in the data’s that that lies beyond this limits so therefore there are no outliers, okay? So we have no outliers for this data set, okay? Alright, so now remember if there is no outlier in the data set, the whiskers drawn to the end of the list are greatest value that is not an outlier, okay, so that is something just to keep in mind. Alright, so now we are ready to draw number line and plot our points, okay? From these each value for step one. So we want to have and plotted our points okay? So I have our median at 38 right? 50.5 is our third quartile or upper quartile right? 22 is our lower quartile, alright, okay. And then we have 17 which is our least value and then we had 56 which is our greatest value alright so I have plotted all my points okay. Now the next step we are going to do is we are going to draw the box and whiskers. Okay so the box is drawn around the quartile values so I am going to put down here and you will see what I am saying. So the box is —the box is drawn around the quartile values okay? So we have our lower quartile our median and our upper quartile and that is where the box is drawn okay? It extends from the lower quartile to the upper and divide the box by the vertical line, okay, so where the median is. So there is our vertical line where the median is, okay? Now, the whiskers extend from each quartile to the extreme data point, okay, so we have the upper quartile and the whisker goes to our extreme. So the upper quartile goes to the largest value, your lower quartile the whisker goes to the smallest value, okay? One of the whiskers is drawn from the lower quartile to the smallest quartile right? And then the other whisker is drawn from your upper quartile to the largest value, alright? So now we have our box and whisker plot. So the second question asked is what is to the link of the spots and whisker plot tell you about the data? Well, a long whisker indicates that the data and the quartile are quartiles have a greater range so if you have a long whisker, okay, in the quartile quartiles you have a greater range, okay? A shorter whisker would then indicate that the data in the quartile or quartiles have a lesser range okay so if you have a shorter whisker that means you have a lesser range, okay? Similarly, a long box okay indicates that the data in the quartile or quartiles have a greater range okay and a shorter box indicates that the data in the quartile or quartiles have a lesser range, okay? The medium line seems to divide the box into two approximately equal parts so the data and the second and third quartiles are similarly spread out. The whiskers at the right and the left are almost equal in length so the data and the tip in the first and fourth quartiles are similarly spread out. Alright, keep in mind things to remember, a box and whisker plot shows the distribution of data it separates data into four equal parts. The middle half of the data is represented by a box with a vertical line at the median, okay, and let’s go back shows picture. Okay so the middle half of the data is represented by a box of the vertical line at the median. The lower quartile and upper quartile are represented by whiskers that extend to the smallest and largest value. A long whisker, okay, indicates that the data in that quartile or quartiles have a greater range. A shorter whisker indicates that the data in that quartile or quartiles have a lesser range. If there is an outliner in the data, the whisker is drawn till the end of the least greatest value, that is not an outlier.

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